Volume 13, issue 3 (2009)

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The Seiberg–Witten equations and the Weinstein conjecture II: More closed integral curves of the Reeb vector field

Clifford Henry Taubes

Geometry & Topology 13 (2009) 1337–1417
Abstract

Let $M$ denote a compact, orientable 3–dimensional manifold and let a denote a contact 1–form on $M$; thus a $\wedge$ da is nowhere zero. This article explains how the Seiberg–Witten Floer homology groups as defined for any given ${Spin}_{ℂ}$ structure on $M$ give closed, integral curves of the vector field that generates the kernel of $da$.

Mathematical Subject Classification 2000
Primary: 57R17, 57R57
Publication
Revised: 24 November 2008
Accepted: 1 December 2008
Published: 16 February 2009
Proposed: Tom Mrowka
Seconded: Yasha Eliashberg, Ron Stern
Authors
 Clifford Henry Taubes Department of Mathematics Harvard University Cambridge MA 02138 USA